A model train with a mass of #7 kg# is moving along a track at #12 (cm)/s#. If the curvature of the track changes from a radius of #32 cm# to #36 cm#, by how much must the centripetal force applied by the tracks change?

Question

A model train with a mass of #7  kg# is moving along a track at #12 (cm)/s#.  If the curvature of the track changes from a radius of #32 cm# to #36 cm#, by how much must the centripetal force applied by the tracks change?

Adrian Ayala · Accepted Answer

The change in centripetal force is #=0.035N#

Centripetal force is what

#vecF_C=(mv^2)/r*vecr#

The mass is of the train #m=7kg#

The velocity of the train is #v=0.12ms^-1#

The tracks' respective radii are

#r_1=0.32m#

additionally

#r_2=0.36m#

The centripetal force's variance is

#DeltaF=F_2-F_1#

What are the centripetal forces?

#||F_1||=7*0.12^2/0.32=0.315N#

#||F_2||=7*0.12^2/0.36=0.280N#

#DeltaF=F_1-F_2=0.315-0.280=0.035N#

Nora Arzate · Answer

undefined To find the change in centripetal force, we first need to calculate the centripetal force exerted by the tracks on the model train before and after the change in curvature. Centripetal force can be calculated using the formula:

F = (m * v^2) / r

Where:
F = centripetal force
m = mass of the object (7 kg in this case)
v = velocity of the object (12 cm/s)
r = radius of the curvature (before and after the change)

Before the change:
r1 = 32 cm
F1 = (7 * 12^2) / 32

After the change:
r2 = 36 cm
F2 = (7 * 12^2) / 36

Change in centripetal force = F2 - F1